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What do you mean by geodesics?
In geometry, a geodesic (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) is commonly a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold.
How do you calculate geodesics?
A curve α : I → S parametrized by arc length is called a geodesic if for any two points P = α(s1),Q = α(s2) on the curve which are sufficiently close to each other, the piece of the trace of α between P and Q is the shortest of all curves in S which join P and Q.
What are geodesic equations?
Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity, that results in obtaining geodesics.
What are geodesics on a sphere?
A geodesic is a locally length-minimizing curve. On the sphere, the geodesics are great circles (like the equator). The geodesics in a space depend on the Riemannian metric, which affects the notions of distance and acceleration. Geodesics preserve a direction on a surface (Tietze 1965, pp.
Where can I find timelike geodesics?
If a geodesic α is timelike, then dτ/dρ = constant, and we have ρ = aτ + b for some a and b.
What are the geodesics on the surface?
Geodesics are curves of shortest distance on a given surface. Apart from their intrinsic interest, they are of practical importance in the transport of goods and passengers at minimal expense of time and energy.
Why are great circles geodesics?
It’s because planes travel along the shortest route in a 3-dimensional space. This route is called a geodesic or great circle route. They are common in navigation, sailing and aviation.
What does timelike geodesic mean?
Definition. A geodesic α is timelike, lightlike, or spacelike according to whether ( α∨, α∨) is positive, zero, or negative.